WHAT HAVE House Republicans managed to accomplish in a week of government shutdown?

Damage the livelihood of millions of Americans? Check. Government secretaries, food-truck operators, cleaners who work in motels near national parks: They’re all hurting.

Waste billions of taxpayer dollars? Check. It costs a lot to shut agencies, Web sites and parks, and it will cost a lot to reopen them. Meanwhile, the House has voted to pay the salaries, eventually, of hundreds of thousands of employees whom it has ordered not to work. That’s an odd way to manage an enterprise.

Interfere with key government operations? Check. The National Transportation Safety Board can’t investigate an accident last weekend on Metro’s Red Line that claimed the life of a worker. That could make future accidents more likely. On the other side of the world, U.S. allies from Tokyo to Singapore are wondering whether they can rely on a nation whose president has to go AWOL from a key summit meeting in their region.

Rattle the markets, slow an economy in recovery, interrupt potentially lifesaving research at the National Institutes of Health? Check, check and check.

Derail the hated Obamacare? Ch . . . — oh, no, wait a minute. That was the GOP’s ostensible purpose for this travesty of misgovernment, but the online insurance markets created by that law opened on schedule last week and continue to operate. In fact, the Republicans managed only to distract attention from the computer glitches that would have gobbled up all the news attention if the government weren’t shut.

In a revealing moment Sunday on ABC’s “This Week,” host George Stephanopoulos replayed a clip from last year in whichHouse Speaker John A. Boehner (R-Ohio) explained the foolishness of the tactic that he is now, a year later, pursuing. “It’s pretty clear that the president was reelected,” Mr. Boehner said then. “Obamacare is the law of the land. If we were to put Obamacare into the CR [continuing resolution] and send it over to the Senate, we were risking shutting down the government. That is not our goal.”

Cowed by Sen. Ted Cruz (R-Tex.) and bullied by the most conservative members of his caucus, Mr. Boehner has done exactly what he said made no sense. Now he doesn’t know how to get out of the predicament. A shutdown is bad; a default on the debt, which looms 10 days from now, could be catastrophic. The speaker is demanding that President Obama negotiate, while setting “red lines” for those hypothetical talks (“Very simple. We’re not raising taxes.”). It’s not an impressive strategy.

At some point, Mr. Obama and the Democrats will have to throw the speaker a lifeline. As tempted as they may be to see the Republicans blamed for economic disaster, giving the Democrats a chance to recapture the House in 2014, the potential damage to the nation is too great — and Americans could end up blaming everyone who seems to have a hand in this mess. A temporary extension of the debt ceiling, a reopening of the government and a commitment to engage in a process that leads to budget and tax reform: The ingredients of a deal are there.

But throwing a lifeline is pointless until the victim realizes he may be drowning. It’s not clear the Republicans have reached that point. The danger is they will take the country down with them.